Automatic program repair seeks to generate correct code from buggy programs, with most approaches searching the correct program in a discrete, symbolic space of source code tokens. This symbolic search is fundamentally limited by its inability to directly reason about program behavior. We introduce Gradient-Based Program Repair (GBPR), a new paradigm that reframes program repair as continuous optimization in a differentiable numerical program space. Our core insight is to compile symbolic programs into differentiable numerical representations, enabling search in the numerical program space directly guided by program behavior. To evaluate GBPR, we present RaspBugs, a new benchmark of 1,466 buggy symbolic RASP programs and their respective numerical representations. Our experiments demonstrate that GBPR can effectively repair buggy symbolic programs by gradient-based optimization in the numerical program space, with convincing repair trajectories. To our knowledge, we are the first to state program repair as continuous optimization in a numerical program space. Our work establishes a new direction for program repair research, bridging two rich worlds: continuous optimization and program behavior.

Published in IEEE Robotics and Automation Letters, vol. Abstract-- This paper presents a new approach for 6DoF Direct LiDAR-Inertial Odometry (D-LIO) based on the simultaneous mapping of truncated distance fields on CPU. Such continuous representation (in the vicinity of the points) enables working with raw 3D LiDAR data online, avoiding the need of LiDAR feature selection and tracking, simplifying the odometry pipeline and easily generalizing to many scenarios. The method is based on the proposed Fast Truncated Distance Field (Fast-TDF) method as a convenient tool to represent the environment, employing binary masks that encodes the L1 distance. Such representation enables i) solving the LiDAR point-cloud registration as a nonlinear optimization process without the need of selecting/tracking LiDAR features in the input data, ii) simultaneously producing an accurate truncated distance field map of the environment, and iii) updating such map at constant time independently of its size. The approach is tested using open datasets, aerial and ground. It is also benchmarked against other state-of-the-art odometry approaches, demonstrating the same or better level of accuracy with the added value of an online-generated TDF representation of the environment, that can be used for other robotics tasks as planning or collision avoidance. Accurate vehicle localization is a crucial aspect of robotics, directly influencing autonomous navigation, remote exploration, and other advanced applications. V arious techniques are employed to improve localization, combining data from different sensors such as cameras, inertial measurement units (IMUs), LiDAR and radar [1].

This degradation persists across standard approaches including supervised fine-tuning (SFT) and reinforcement learning from human feedback (RLHF). While reinforcement learning with verifiable rewards (RL VR) has emerged as a promising alternative that optimizes models on objectively measurable tasks, its safety implications remain unexplored. We present the first comprehensive theoretical and empirical analysis of safety properties in RL VR. Theoretically, we derive upper bounds on safety drift under KL-constrained optimization and prove conditions under which safety degradation is eliminated. Empirically, we conduct extensive experiments across five adversarial safety benchmarks, demonstrating that RL VR can simultaneously enhance reasoning capabilities while maintaining or improving safety guardrails. Our comprehensive ablation studies examine the effects of optimization algorithms, model scale, and task domains. Our findings challenge the prevailing assumption of an inevitable safety-capability trade-off, and establish that a specific training methodology can achieve both objectives simultaneously, providing insights for the safe deployment of reasoning-capable LLMs.

Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex setting and develop new hard instances that yield nontrivial lower bounds under deterministic and stochastic first-order oracle models. In the deterministic case, we prove that any first-order zero-respecting algorithm requires at least $Ω(κ^{3/2}ε^{-2})$ oracle calls to find an $ε$-accurate stationary point, improving the optimal lower bounds known for single-level nonconvex optimization and for nonconvex-strongly-convex min-max problems. In the stochastic case, we show that at least $Ω(κ^{5/2}ε^{-4})$ stochastic oracle calls are necessary, again strengthening the best known bounds in related settings. Our results expose substantial gaps between current upper and lower bounds for bilevel optimization and suggest that even simplified regimes, such as those with quadratic lower-level objectives, warrant further investigation toward understanding the optimal complexity of bilevel optimization under standard first-order oracles.

The widespread use of neural surrogates in automotive aerodynamics, enabled by datasets such as DrivAerML and DrivAerNet++, has primarily focused on bluff-body flows with large wakes. Extending these methods to aerospace, particularly in the transonic regime, remains challenging due to the high level of non-linearity of compressible flows and 3D effects such as wingtip vortices. Existing aerospace datasets predominantly focus on 2D airfoils, neglecting these critical 3D phenomena. To address this gap, we present a new dataset of CFD simulations for 3D wings in the transonic regime. The dataset comprises volumetric and surface-level fields for around $30,000$ samples with unique geometry and inflow conditions. This allows computation of lift and drag coefficients, providing a foundation for data-driven aerodynamic optimization of the drag-lift Pareto front. We evaluate several state-of-the-art neural surrogates on our dataset, including Transolver and AB-UPT, focusing on their out-of-distribution (OOD) generalization over geometry and inflow variations. AB-UPT demonstrates strong performance for transonic flowfields and reproduces physically consistent drag-lift Pareto fronts even for unseen wing configurations. Our results demonstrate that AB-UPT can approximate drag-lift Pareto fronts for unseen geometries, highlighting its potential as an efficient and effective tool for rapid aerodynamic design exploration. To facilitate future research, we open-source our dataset at https://huggingface.co/datasets/EmmiAI/Emmi-Wing.

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a suitable approximation. Beyond making the resulting network less transparent, overparameterization creates a large optimization space, likely producing local minima in training that have quite different generalization errors. In this case, network initialization can have an outsize impact on the model's out-of-sample accuracy. For these reasons, we propose shallow universal polynomial networks (SUPNs). These networks replace all but the last hidden layer with a single layer of polynomials with learnable coefficients, leveraging the strengths of DNNs and polynomials to achieve sufficient expressivity with far fewer parameters. We prove that SUPNs converge at the same rate as the best polynomial approximation of the same degree, and we derive explicit formulas for quasi-optimal SUPN parameters. We complement theory with an extensive suite of numerical experiments involving SUPNs, DNNs, KANs, and polynomial projection in one, two, and ten dimensions, consisting of over 13,000 trained models. On the target functions we numerically studied, for a given number of trainable parameters, the approximation error and variability are often lower for SUPNs than for DNNs and KANs by an order of magnitude. In our examples, SUPNs even outperform polynomial projection on non-smooth functions.

In recent years, dual-arm manipulation has become an area of strong interest in robotics, with end-to-end learning emerging as the predominant strategy for solving bimanual tasks. A critical limitation of such learning-based approaches, however, is their difficulty in generalizing to novel scenarios, especially within cluttered environments. This paper presents an alternative paradigm: a sampling-based optimization framework that utilizes a GPU-accelerated physics simulator as its world model. We demonstrate that this approach can solve complex bimanual manipulation tasks in the presence of static obstacles. Our contribution is a customized Model Predictive Path Integral Control (MPPI) algorithm, \textbf{guided by carefully designed task-specific cost functions,} that uses GPU-accelerated MuJoCo for efficiently evaluating robot-object interaction. We apply this method to solve significantly more challenging versions of tasks from the PerAct$^{2}$ benchmark, such as requiring the point-to-point transfer of a ball through an obstacle course. Furthermore, we establish that our method achieves real-time performance on commodity GPUs and facilitates successful sim-to-real transfer by leveraging unique features within MuJoCo. The paper concludes with a statistical analysis of the sample complexity and robustness, quantifying the performance of our approach. The project website is available at: https://sites.google.com/view/bimanualakslabunitartu .

Fair clustering has gained increasing attention in recent years, especially in applications involving socially sensitive attributes. However, existing fair clustering methods often lack inter-pretability, limiting their applicability in high-stakes scenarios where understanding the rationale behind clustering decisions is essential. In this work, we address this limitation by proposing an interpretable and fair clustering framework, which integrates fairness constraints into the structure of decision trees. Our approach constructs interpretable decision trees that partition the data while ensuring fair treatment across protected groups. To further enhance the practicality of our framework, we also introduce a variant that requires no fairness hyperparameter tuning, achieved through post-pruning a tree constructed without fairness constraints. Extensive experiments on both real-world and synthetic datasets demonstrate that our method not only delivers competitive clustering performance and improved fairness, but also offers additional advantages such as interpretability and the ability to handle multiple sensitive attributes. These strengths enable our method to perform robustly under complex fairness constraints, opening new possibilities for equitable and transparent clustering.

Mixed Integer Linear Programming (MILP) is a fundamental class of NP-hard problems that has garnered significant attention from both academia and industry. The Branch-and-Bound (B\&B) method is the dominant approach for solving MILPs and the branching plays an important role in B\&B methods. Neural-based learning frameworks have recently been developed to enhance branching policies and the efficiency of solving MILPs. However, these methods still struggle with semantic variation across depths, the scarcity of upstream nodes, and the costly collection of strong branching samples. To address these issues, we propose \ours, a Dynamic \underline{\textbf{S}}tratified \underline{\textbf{C}}ontrastive Training Framework for \underline{\textbf{MILP}} Branching. It groups branch-and-bound nodes based on their feature distributions and trains a GCNN-based discriminative model to progressively separate nodes across groups, learning finer-grained node representations throughout the tree. To address data scarcity and imbalance at upstream nodes, we introduce an upstream-augmented MILP derivation procedure that generates both theoretically equivalent and perturbed instances. \ours~effectively models subtle semantic differences between nodes, significantly enhancing branching accuracy and solving efficiency, particularly for upstream nodes. Extensive experiments on standard MILP benchmarks demonstrate that our method enhances branching accuracy, reduces solving time, and generalizes effectively to unseen instances.